Bill Hawkins wrote:
I'm picturing 100,000 pendula in a cave, all gravity locked to
their neighbors. (How small would they have to be to fit into
the main cave at Carlsbad Caverns, New Mexico?)

Gravity-lock? Wouldn't just the ordinary sound-waves be sufficient?

With a pendulum there will be mechanical bending and torsion as it swings here and there... here and there... far more likely than the gravity shift of the swings.

Regardless, even for well balanced, counter-swinging and whatever, putting distance between two clocks will reduce both acoustical and gravity coupling between them. Acoustical damping adapted to the pendulum rate would also help, both as a transmitter and as a receiver, just as with any EMC case.

Cheers,
Magnus

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